German Patent Application No. 196 09 717 describes an arrangement for detecting roll-over occurrences in vehicles. In case roll-over of a vehicle occurs, all passenger protection devices installed in the vehicle must be triggered promptly, including, for example, roll bars, belt tighteners and various airbags. To enable prompt triggering of all of these protection devices, it must be detected as soon as possible whether rotations of the vehicle about its vertical axis, its longitudinal axis or its transverse axis lead to a roll-over. Incorrect decisions on a roll-over occurrence must be ruled out insofar as possible so that the restraint devices are not triggered when, for example, the vehicle is on a steep slope or undergoes slow rotational occurrences during travel through curves. To prevent incorrect decisions from occurring in the roll-over sensing, the inertial state, i.e., the initial state of the vehicle relative to the earth-based coordinate system, must be known. Dynamic vehicle movements such as travel through curves or braking or acceleration procedures can have disruptive effects in determining the inertial state.